Long free-response question

Dissolving ammonium nitrate

Units 6 and 9
10 points
About 23 minutes

You can use a calculator on this question, just like on exam day.

A multipart question, often built around a lab setup or a data table, that mixes several topics. You calculate, explain and justify your answers across many lettered parts. On the exam: 3 questions (Questions 1–3), part of the 1-hour-45-minute free-response section; calculator allowed.

The question and its sources

Instant cold packs work because ammonium nitrate absorbs energy as it dissolves in water: NH₄NO₃(s) → NH₄⁺(aq) + NO₃⁻(aq).

Calorimetry experiment

A student adds 5.00 g of NH₄NO₃(s) (molar mass 80.05 g/mol) to 100.0 g of water at 23.50 °C in a foam-cup calorimeter and stirs until the solid dissolves. The lowest temperature reached is 19.80 °C.

Assume the solution has a mass of 105.0 g and a specific heat of 4.18 J/(g·°C), and that the calorimeter itself absorbs no heat.

Source: Hypothetical data

Table 1. Standard thermodynamic data at 298 K

Substance	ΔH°f (kJ/mol)	S° (J/(mol·K))
NH₄NO₃(s)	−365.6	151.1
NH₄⁺(aq)	−132.5	113.4
NO₃⁻(aq)	−205.0	146.4

Source: Standard reference values, rounded

Suggested time: 23 minutes

Your answers are saved in this browser as you type.

Part (a)

2 points

Using the calorimetry data, (i) calculate the amount of heat, in joules, that the water lost to the dissolving NH₄NO₃, and (ii) calculate the experimental value of ΔH_soln, in kJ/mol.

Your answer to part (a)

0 / 2,500 characters

Part (b)

1 point

Use the data in Table 1 to calculate ΔH° for the dissolving of NH₄NO₃(s).

Your answer to part (b)

0 / 2,500 characters

Part (c)

1 point

The experimental value from part (a) is smaller than the value calculated in part (b). Identify one specific source of experimental error that could account for this difference, and explain how it would lead to a smaller value of ΔH_soln.

Your answer to part (c)

0 / 2,500 characters

Part (d)

1 point

Without performing a calculation, predict whether ΔS° for the dissolving of NH₄NO₃(s) is positive or negative. Justify your prediction.

Your answer to part (d)

0 / 2,500 characters

Part (e)

1 point

Use the data in Table 1 to calculate ΔS° for the dissolving of NH₄NO₃(s).

Your answer to part (e)

0 / 2,500 characters

Part (f)

1 point

Calculate ΔG° for the dissolving of NH₄NO₃(s) at 298 K.

Your answer to part (f)

0 / 2,500 characters

Part (g)

1 point

Is the dissolving of NH₄NO₃(s) thermodynamically favorable at 298 K? Explain whether the enthalpy change or the entropy change is responsible for the answer.

Your answer to part (g)

0 / 2,500 characters

Part (h)

1 point

Calculate the value of the equilibrium constant, K, for the dissolving of NH₄NO₃(s) at 298 K.

Your answer to part (h)

0 / 2,500 characters

Part (i)

1 point

Explain why the dissolving of NH₄NO₃(s) in water is endothermic, in terms of the interactions that are broken and formed.

Your answer to part (i)

0 / 2,500 characters

Checking scoring…

Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.